Self-assembled edifices play an important role in the development of novel nanostructured materials. Among them, the simplest, most organized and most robust are certainly those which spontaneously form block copolymers as they adopt, during simple annealing operations at temperatures of the order of 150° C., particularly regular periodical composite structures of lamellae, cylinders or spheres which endure in the solid state when they are cooled to normal temperature. The mechanisms which underlie this self-assembling are largely independent of the exact chemical nature of the copolymers and the pitch of the structure can be adjusted typically between 5 and 100 nm by varying only the length of the blocks. The number of applications of the block copolymers, used pure or mixed with homopolymers or solvents, is immense and, whether they are compatibilizing agents for elastomeric materials, biocompatible materials, ultraresistant plastics, adhesives, manufacturing techniques in microelectronics or in micro- and nanotechnologies, manufacture of nanoporous or nanostructured materials (hydrogen storage, catalysis, photonic crystals, and the like), their chemical variety is very high.
Mention may be made, by way of example, of the following review articles:    1) Anne-Valérie Ruzette and Luwik Leibler, Nature Materials, 4, pp. 19-31 (2005), “Block copolymers in tomorrow's plastics”;    2) Ludwik Leibler, Prog. Polym. Sci., 30 (2005), 898-914, “Nanostructured plastics: Joys of self-assembling”;    3) Cheolmin Park, Jongseung Yoon and Edwin L. Thomas, Polymer, 44 (2003), 6725-6760, “Enabling nanotechnology with self-assembled block copolymer patterns”;    4) Leonard Pinchuk, Gregory J. Wilson, James J. Barry, Richard T. Schoephoerster, Jean-Marie Parel and Joseph P. Kennedy, Biomaterials, 29 (2008);    5) Sang Ouk Kim, Harun H. Solak, Mark P. Stoykovich, Nicola J. Ferrier, Juan J. de Pablo and Paul F. Nealey, Nature, 424 (2003), 411-414;    6) Massimo Lazzari and M. Arturo Lopez-Quintela, Advanced Materials, 15 (19), 1583-1594 (2003), “Block Copolymers as a Tool for Nanomaterial Fabrication”;    7) Costantino Creton, Guangjun Hu, Fanny Deplace, Leslie Morgret and Kenneth R. Shull, Macromolecules, 42, (2009), 7605-7615;    8) Yu-Chih Tseng and Seth B. Darling, Polymers 2010, 2, 470-489, “Block Copolymer Nanostructures for Technology”;    9) Ho-Cheol Kim, Sang-Min Park and William D. Hinsberg, Chem. Rev., 110, pp. 146-177, “Block Copolymer Based Nanostructures: Materials, Processes and Applications to Electronics”;    10) Ho, Fan, Tseng, Chiang, Lin, Ko, Huang, Shih and Chen, U.S. Pat. No. 7,632,544 B2 (2009), “Nanopatterned templates from oriented degradable diblock copolymer thin films”;    11) Nikos Hadjichristidis, Hermis Latrou, Marinos Pitsikalis, Stergios Pispas and Apostolos Avgeropoulos, “Linear and non-linear triblock terpolymers. Synthesis, self-assembly in selective solvents and in bulk”, Prog. Polym. Sci., 30 (2005), 725-782.
FIGS. 1A-1C illustrate the various lamellar structures known from the prior art which can be formed by an AB diblock copolymer. It will be assumed, in the systematic description, that the two blocks are immiscible, which is generally the case with two polymers having different chemical natures, and that they have the same length and the same volume. The free energy F per chain of this system, the minimum of which describes the equilibrium configuration, is written as the sum of two terms: F=γABΣ+Fel. See, in this connection:    12) Alexander, S. J. Phys. (Paris), 38 (1977), p. 983;    13) de Gennes, P. G., Macromolecules, 13 (1980), p. 1069;    14) Abetz, V., Stadler, R. and Leibler, L., Polym. Bull., 37 (1996), p. 135;    15) Birshtein, T. M., Polotsky, A. A. and Amoskov, V. M., Macromol. Symp., 146 (1999), p. 215;    16) Semenov, A. N. and Rubinstein, M., Macromolecules, 1998, 31, 1373;    17) I. Ya. Erukhimovich, M. V. Belousov, E. N. Govorun, V. Abetz and M. V. Tamm, “Non-Centrosymmetric Lamellar Structures in the Associating Blends of Tri- and Diblock Copolymers”, Macromolecules, 43 (2010), pp. 3465-3478;    18) Semenov, A. N., 1985, Soviet Phys. JETP, 61, 733;    19) Milner, S. T., Witten, T. A. and Cates, M. E., 1988, Europhys. Lett., 5, 413;    20) Milner, S. T., Witten, T. A. and Cates, M. E., 1988, Macromolecules, 21, 2610;    21) Milner, S. T., Witten T. A. and Cates, M. E., 1988, Macromolecules, 22, 853;    22) Milner, S. T. and Witten, T. A., 1988, J. Phys. Paris, 19, 1951    23) Yang Yuliang, Qiu Feng, Tang Ping and Zhang Hongdong, Science in China: Series B Chemistry (2006), Vol. 49, No. 1, 21-43    24) M. W. Matsen and F. S. Bates, “Unifying strong- and weak-segregation block copolymer theories”, Research Report UMSI 95/164 (1995)    25) M. W. Matsen and M. Schick, Phys. Rev. Letters, 72 (16), pp. 2660-2663 (1994).
The first term represents the contact energy between A and B, that is to say the product of their interfacial tension and the contact area per chain. It decreases when the chains stretch perpendicularly to the lamellae and this stretching is reflected by the presence of the second term, which describes an elastic energy. At equilibrium, these two terms observe the rule of equipartition in the three directions of space. They respectively represent ⅔ and ⅓ of the total energy, which is thus written F=(3/2) γABΣ. By dividing the energy per chain by the molecular volume Σl, l denoting the height of a molecule, a particularly simple expression is obtained for the volume energy density of the material, which is
  f  =                              3          2                ⁢                  γ          AB                    l        .  It shows that this density is simply proportional to the number of interfaces per unit of length along z, z being an axis normal to the lamellae. In order to form as few AB interfaces as possible, the lamellar order is periodic and composed of bilayers. It is written AB/BA/AB/BA . . . . This structure, illustrated in FIG. 1A, is symmetric. Its energy is virtually half that of the competing nonsymmetric order AB/AB/AB/AB, represented in FIG. 1B, since it comprises virtually half as many AB interfaces per unit of volume (“virtually” only, because the equilibrium thickness of the lamellae is greater, which is not taken into account in the figures). In fact, this non-centrosymmetric order has never been observed in practice.
FIG. 1C illustrates a defect of stacking in the symmetric structure of FIG. 1A. Defects of this type exhibit an energy which is too high to be stable, which explains the nonexistence in practice of the non-centrosymmetric structure of FIG. 1B.
In the figures, the references 1 and 1′ indicate “realistic” representations in which the diblocks are represented in the form of entangled linear chains, while the references 2, 2′ and 2″ indicate more diagrammatic representations.
More generally, the block sequential copolymers organize themselves according to the following rule: two chemically similar (referred to simply as “similar”) sequences tend to unite and two chemically different sequences tend to separate. The associating of similar sequences takes place both laterally (by entangling of similar neighboring blocks) and longitudinally (by interpenetration of similar end blocks); see    26) F. S. Bates and G. H. Fredrickson, “Block Copolymer Thermodynamics—Theory and Experiment”, Annual Review of Physical Chemistry, 41, p. 525 (1990).
Inside a bilayer, the similar blocks A and B of the molecules in contact are assembled. Subsequently, the term “chemical dipolar interaction” will be used to describe this double association of molecules via the two blocks A and B.
It should be pointed out that the individual bilayers are not connected to one another, which is reflected by a low resistance of the material to shearing.
As explained above, for energy reasons, these materials virtually exclusively form centrosymmetric self-assembled structures. In point of fact, many applications of great technological interest require non-centrosymmetric (NCS) structures which make it possible to obtain materials exhibiting a second-order nonlinear optical response (for the production of components for optical telecommunications and integrated optics), piezoelectric properties (for sensors or actuators), pyroelectric properties (for detectors), a ferromagnetic or ferroelectric behavior, and the like.
This is why a very particular effort has been undertaken for about twenty years in an attempt to obtain self-assembled materials based on copolymers exhibiting a non-centrosymmetric order, this being the case in particular in lamellar structures where this order is expressed simply by an absence of symmetry with respect to the +z and −z directions.
The first NCS structure of a material formed of block copolymers is due to Goldacker et al.    27) Thorsten Glacer, Volker Abetz, Reimund Stadler, Igor Erukhimovich and Ludwik Leibler, “Non-centrosymmetric superlattices in block copolymer blends”, Nature, 398 (1999), pp. 137-139.
It is composed of a mixture of an ABC triblock and an ac diblock, the small letters representing markedly shorter blocks than the capital letters. The NCS order is based on the following properties:                The interfacial tension between two similar entities (γAA, γBB), which can be negative, exhibits in all cases a very low modulus with respect to the interfacial tension—positive—between two immiscible entities (γAB . . . ).        The interfacial tension for interpenetration between chemically similar blocks having different length (such as γAa and γBb) is algebraically lower (in algebraic value) than the interpenetration tension between similar blocks having the same length (γAA, γBB).        
To simplify, in the continuation, γAB=γAC=γBC=γ will be set down.
Due to these properties, the stack ABC/ca/ABC/ca . . . is slightly favored on the energy level, with respect to the stack ABC/CBA/ac/ca/ABC/CBA/ac/ca . . . or to any other stack comprising bilayers, and the NCS structure is predominantly present. In these materials, the NCS order thus rests on a very slight preference, which means that the centrosymmetric order is also present in a noninsignificant proportion. Furthermore, the intercalation of a simple bilayer, such as ca/ac, in the structure is sufficient to reverse the ABC order into the CBA order via an ABC/ca/ac/CBA sequence. This defect of stacking does not require any additional interface between immiscible entities. The associated energy is very low and the defect is frequent. This results in materials composed of microscopic domains having both centrosymmetric and non-centrosymmetric structure, in which, furthermore, the non-centrosymmetric regions exhibit frequent reversals of polarity. This solution is thus not readily applicable to the manufacture of monodomain NCS samples of macroscopic size (dimensions greater than or equal to 1 mm).
An alternative form of this material was recently proposed in a theoretical work by Erukimovich et al. (abovementioned reference 17). It consists in fixing the associations between long and short blocks, such as A and a, by groups which are donating/accepting with respect to the chain ends. This alternative form is more complicated from a chemical viewpoint. It is also difficult to implement as the encounter between two complementary ends is of very low probability. Finally, this solution makes it possible only to fix the self-assembled structure which has formed beforehand and which, as has been explained above, comprises numerous defects.
Another example of preferably non-centrosymmetric material was obtained by Takano et al.:    28) A. Takano, K. Soga, J. Suzuki and Y. Matsushita, “Noncentrosymmetric Structure from a Tetrablock Quarterpolymer of the ABCA Type”, Macromolecules, 36 (2003), pp. 9288-9291.
The material is pure and composed of ABCA tetrablocks, with two A blocks of the same length. It is preferably arranged according to the lamellar sequence ABCA/ABCA/ABCA . . . rather than according to ABCA/ACBA/ABCA . . . . The reason for this is a slight asymmetry between the lengths of the B and C blocks which leads the ends A to adopt different degrees of stretching, then behaving as if they had different lengths. The mechanism is thus very similar to that of the preceding example. Here again, there exists competing symmetric orders and the preference for the non-centrosymmetric order remains very slight.
Another example has been obtained by Abetz and Goldacker with a mixture of two triblocks identical in composition but having central blocks of unequal length. In this example, the interpenetration is monopolar (adjacent molecules in the material are bonded to one another via interactions between one block only of each said molecule) and the material is full of defects and is brittle:    29) Volker Abetz and Thorsten Goldacker, Macromol. Rapid Commun., 21, 16-34 (2000).
The same authors in the same paper also reported that a mixture in equal parts of two ABC and BAC triblocks exhibits a mixture of symmetric and nonsymmetric regions, with here again many defects.
Also, in these four examples, the layers are still unconnected and can easily slide over one another, resulting in a high mechanical brittleness.
Yet another example of a preferably non-centrosymmetric material has been given by Stupp et al.:    30) S. I. Stupp, V. LeBonheur, K. Walker, L. S. Li, M. Keser and A. Amstutz, Science, 276 (1997), p. 384;    31) Leiming Li and Samuel I. Stupp, Applied Physics Letters, 78 (26), pp. 4127-4129 (2001).
These self-assembled materials are formed of diblocks or triblocks in which at least one block is rigid. The molecules associate together in “bouquets” which are subsequently arranged head to tail and are encountered stacked parallel and oriented in the same direction. Films of a few hundred layers have thus been obtained with a polar arrangement but their χ(2) coefficient (second-order nonlinear electric susceptibility) remains low. Furthermore, their chemical synthesis is very unwieldy, which excludes any industrial use. Finally, experience shows that these materials can with difficulty receive hyperpolarizable groups capable of strongly modifying their χ(2) coefficient.